How do you prove $(1-tan^2theta)/(1-cot^2theta)=1-sec^2theta$ ?

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Answer 1 · 2016-10-05T17:56:56

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$(1-tan^2 theta)/(1-cot^2 theta)=1-sec^2 theta$

Left Side: $=(1-tan^2 theta)/(1-cot^2 theta)$

$=(1-tan^2 theta)/(1-1/tan^2 theta)$

$=(1-tan^2 theta)/((tan^2theta-1)/tan^2 theta)$

$=(1-tan^2 theta) * (tan^2 theta)/(tan^2theta-1)$

$=(1-tan^2 theta) * (tan^2 theta)/-(1-tan^2theta)$

$=-tan^2 theta$

$=-(sec^2theta-1)$

$=-sec^2theta +1$

$=1-sec^2 theta$

$=$ Right Side

How do you prove (1-tan^2theta)/(1-cot^2theta)=1-sec^2theta(1-tan^2theta)/(1-cot^2theta)=1-sec^2theta?